Research Interests

My research interests are in the area of scientific computing, with a focus on computational partial differential equations and variational problems. Specific applications include plasma physics, solid-mechanics, liquid crystals, porous media, and other complex fluid and electromagnetic problems. I am interested in both physical modeling as well as numerical computation using various finite-element methods and multigrid.

Here is a list of my Publications. and here are some "cool", but now somewhat dated movies of my past research.

Software

Together with Xiaozhe Hu (Tufts) and Ludmil Zikatanov (Penn State), I am one of the authors of HAZmath: A Simple Finite Element, Graph, and Solver Library, which provides basic finite element and graph routines.

PhD Students

Current Students

• Anca Andrei

A list of the PhD students that I have advised or co-advised in the past is found on the Mathematics Genealogy Project.

Computational and Applied Mathematics Seminar

Each semester, I help co-organize a research seminar with graduate students and faculty on computational and applied mathematics.
The meetings can be informal, but often include an invited speaker. See website for more details.

Invited Talks and Visits

Plenary/Keynote Speaker

• Plenary Speaker - 11th International Conference on Large-Scale Scientific Computations
  June 7, 2017 - Sozopol, Bulgaria
  Energy-Minimization, Finite Elements, and Multilevel Methods for Liquid Crystals

Invited Workshop Talks

• NSF CompMath PI Meeting at U. of Washington
  July 16, 2024 - Seattle, WA
  A New Decoupled Solution Method for a Novel Oscillation-Free Numerical Scheme for Biot's Model


• Numerical Methods and New Perspectives for Extended Liquid Crystalline Systems Workshop at ICERM
  December 9, 2019 - Providence, RI
  Energy-Minimization, Finite Elements, and Multilevel Methods for Nematic Liquid Crystals


• Eighth Singular Days:
  June 28, 2016 - Nancy, France
  Graded Mesh Approximation in Weighted Sobolev Spaces and Elliptic Equations in 2D


• Minimum Residual and Least-Squares Finite-Element Methods Workshop:
  November 2, 2015 - Delft, Netherlands
  A First-Order System Petrov-Galerkin Discretization for Singularly Perturbed Reaction-Diffusion


• Workshop on Finite Element Methods - Beijing Institute for Scientific and Engineering Computing:
  August 8, 2015 - Beijing, China
  An Energy-Minimization Finite-Element Approach for the Frank-Oseen Model of Nematic Liquid Crystals


• Least Squares Finite Elements in Fluid and Solid Mechanics Workshop - Leibniz University
  June 21, 2012 - Hannover, Germany
  Constrained First-Order System Least Squares for Improved Mass Conservation and Complex Fluids


• IMA PI Workshop on Numerical Simulations of Complex Fluids - Penn State University:
  March 3, 2010 - State College, PA
  First-Order System Least Squares Approach to Resistive Magnetohydrodynamics


• AMR08 Applied Mathematics Principal Investigators Meeting:
  October 15, 2008 - Argonne National Laboratory, IL
  Nested Iteration First-Order System Least Squares Algebraic Multigrid on Resistive Magnetohydrodynamics

Short-Term Visits

• Visit to University of Maryland
  Fall 2017 - College Park, MD
  Short-term visit to collaborate with Howard Elman.


• Visit to the National University of Ireland, Galway
  May 11 - 16, 2014 - Galway, Ireland
  Short-term visit to collaborate with Niall Madden


• Visit to University of Colorado at Boulder
  March 30 - April 5, 2014 - Boulder, CO
  Short-term visit to collaborate with Tom Manteuffel


• Visit to University of Illinois at Urbana/Champaign
  January 22, 2014 - Urbana, IL
  Short-term visit to collaborate with Luke Olson


• Visiting Scientist - Penn State University
  November 2013 - State College, PA
  Short-term visit to collaborate with James Brannick, Chun Liu, and Ludmil Zikatanov


• Visiting Scientist - Lawrence Livermore National Laboratory
  September 2013 - September 2014 - Livermore, CA
  Short-term visits to the Center for Applied Scientific Computing (CASC) to collaborate with Panayot Vassilevski


• Visit to Centre de Recerca Matematica (CRM):
  June 11-17, 2011 - Bellaterra, Spain
  Nested Iteration, Algebraic Multigrid and Adaptive Local Refinement for MHD and Complex Fluids


• Visit to Radon Institute for Computational and Applied Mathematics (RICAM):
  May 30-June 4, 2011 - Linz, Austria
  Collaboration with Johannes Kraus

Colloquia/Seminars

• Computational and Applied Mathematics Colloquium - The Pennsylvania State University
  November 1, 2021 - Zoom
  Robust Multilevel Preconditioners for a New Stabilized Discretization of the Poroelastic Equation


• Numerical Analysis & PDEs Seminar - University of Delaware
  April 16, 2021 - Zoom
  Robust Multilevel Preconditioners for a New Stabilized Discretization of the Poroelastic Equation


• Mathematics Colloquium - University of New Mexico
  February 16, 2021 - Zoom
  Robust Multilevel Preconditioners for a New Stabilized Discretization of the Poroelastic Equation


• Mathematics Colloquium - Old Dominion University
  November 12, 2020 - Zoom
  A Stabilized Discretization and Robust Solvers for Poroelasticity


• Applied Mathematics Seminar - University of Georgia
  November 11, 2020 - Zoom
  A Stabilized Discretization and Robust Solvers for Poroelasticity


• Applied Mathematics and Computation Seminar - University of Massachusetts Amherst
  March 10, 2020 - Amherst, MA
  A Stabilized Discretization and Robust Solvers for Poroelasticity


• Numerical Analysis Seminar - University of Maryland College Park
  December 5, 2017 - College Park, MD
  Energy-Minimization, Finite Elements, and Multilevel Methods for Liquid Crystals


• Differential Equations Seminar - University of Maryland Baltimore County
  November 13, 2017 - Baltimore, MD
  Energy-Minimization, Finite Elements, and Multilevel Methods for Liquid Crystals


• Oberseminar in Numerische Mathematik - Univesity of Duisburg-Essen
  May 30, 2017 - Essen, Germany
  Numerical Approximation of Asymptotically Disappearing Solutions of Maxwell's Equations


• Center for Computational Mathematics and Applications Colloquium - Penn State University
  March 20, 2017 - State College, PA
  Energy Minimization and a Deflation Technique for Detecting Multiple Liquid Crystal Equilibrium States


• Department of Mathematics Colloquium - Ithaca College
  November 17, 2016 - Ithaca, NY
  Energy Minimization and a Deflation Technique for Detecting Multiple Liquid Crystal Equilibrium States


• Seminar on Numerical Methods for Partial Differential Equations - MIT
  April 8, 2015 - Cambridge, MA
  An Energy-Minimization Finite-Element Approach for the Frank-Oseen Model of Nematic Liquid Crystals


• Numerical Mathematics Workgroup Seminar - University of Duisburg-Essen
  July 14, 2014 - Essen, Germany
  An Energy-Minimization Finite-Element Approach for the Frank-Oseen Model of Nematic Liquid Crystals


• Center for Computational and Applied Mathematics Lunch Seminar - Purdue University
  January 24, 2014 - West Lafayette, IN
  An Energy-Minimization Finite-Element Approach for the Frank-Oseen Model of Nematic Liquid Crystals


• Center for Computational Mathematics and Applications Colloquium - Penn State University
  February 8, 2013 - State College, PA
  Constrained First-Order System Least Squares for Improved Mass Conservation and Complex Fluids


• Center for Computational Mathematics and Applications Luncheon Seminar - Penn State University
  February 8, 2013 - State College, PA
  Numerical Approximation of Asymptotically Disappearing Solutions of Maxwell's Equations


• Wuerzburg University Seminar
  June 19, 2012 - Wuerzburg, Germany
  First-Order System Least-Squares, Multigrid, and Adaptive Local Refinement for Complex Fluids


• Schlumberger-Tufts Computational and Applied Math Seminar - Schlumberger
  April 10, 2012 - Cambridge, MA
  First-Order System Least-Squares, Multigrid, and Adaptive Local Refinement for Complex Fluids


• Tufts Physics Condensed Matter Seminar Series - Tufts University
  January 19, 2012 - Medford, MA
  Adaptive Finite Elements and Multigrid for Complex Fluids and Magnetohydrodynamics


• Applied and Computational Mathematics Seminar (ACMS) - Dartmouth College:
  January 17, 2012 - Hanover, NH
  Nested Iteration, Algebraic Multigrid, and First-Order Least Squares System Finite-Element Method for Magnetohydrodynamics


• Computational Math Seminar - University of Colorado:
  March 9, 2010 - Boulder, CO
  Energetic Variational Approach for Magnetohydrodynamics